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Canonical Key
exp(3*z)/3-1/3
Closed Form
f(z) = (exp(3*z) - 1)/3

Image domain \(f(\mathbb{D})\)

The image of the unit disk under \(f\): concentric circles \(|z|=r\) and radial spokes mapped through \(f(z)=z+a_2z^2+\dots\); the bold curve is the boundary \(f(e^{i\theta})\). Rendered in your browser from the certified Taylor coefficients - nothing is computed server-side.

Taylor series
r* ≈ 0.900
Radius of starlikeness r* ≈ 0.9000
disproven f is starlike on |z| < r*; the colored disk shows the certified region.

Unit disk explorer - hover to evaluate

Hover over the disk

Related

Facts (1)

Property Kind Params Holds Value / r Status Confidence
S* membership {} r ≤ 0.900 ✗ disproven proven

Verification Runs (3)

Verifier Property Direction Outcome Domain r Witness Engine
boundary_scan_closed_form_v31 starlike disproves pass 0.900 0.95*exp(i*1.922078) boundary_v3.1
pointwise_starlike_iv starlike disproves pass 0.990 [-0.30592682443119806, -0.941545951132202] gft-0.1.0-reaudit-20260610
boundary_scan_closed_form starlike disproves pass 0.900 0.95*exp(i*1.922078) boundary_v3.0

Instances (1)

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